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Oscillation tests for linear difference equations with non-monotone arguments

In: Tatra Mountains Mathematical Publications, vol. 79, no. 2
George E. Chatzarakis - Said R. Grace - Irena Jadlovská

Details:

Year, pages: 2021, 81 - 100
Language: eng
Keywords:
non-monotone argument, retarded argument, advanced argument, oscillation, Gr\"{o}nwall inequality
Article type: Mathematics
Document type: scientific paper
About article:
This paper presents sufficient conditions involving $\lim \sup $ for the oscillation of all solutions of linear difference equations with general deviating argument of the form \begin{equation*} Δ x(n)+p(n)x(τ (n))=0, n\in\mathbb{N}0 [ \nabla x(n)-q(n)x(σ (n))=0, n\in \mathbb{N} ], \end{equation*} where \begin{align*} (p(n))n≥ 0 and (q(n))n≥ 1 are sequences of nonnegative real numbers and (τ (n))n≥ 0, (σ (n))n≥ 1 \end{align*} are (not necessarily monotone) sequences of integers. The results obtained improve all well-known results existing in the literature and an example, numerically solved in MATLAB, illustrating the significance of these results is provided.
How to cite:
ISO 690:
Chatzarakis, G., Grace, S., Jadlovská, I. 2021. Oscillation tests for linear difference equations with non-monotone arguments. In Tatra Mountains Mathematical Publications, vol. 79, no.2, pp. 81-100. 1210-3195. DOI: https://doi.org/10.2478/tmmp-2021-0021

APA:
Chatzarakis, G., Grace, S., Jadlovská, I. (2021). Oscillation tests for linear difference equations with non-monotone arguments. Tatra Mountains Mathematical Publications, 79(2), 81-100. 1210-3195. DOI: https://doi.org/10.2478/tmmp-2021-0021
About edition:
Publisher: Mathematical Institute, Slovak Academy of Sciences, Bratislava
Published: 20. 12. 2021
Rights:
https://creativecommons.org/licenses/by-nc-nd/4.0/